Ok, from the document page 16 example at: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.219.2389&rep=rep1&type=pdf
which states:
Any algebraic factor base A can be represented by pairs (r, p) where p is a prime and r satisfies f(r) ≡ 0 (mod p) (Theorem 2.3). Arbitrarily, let p be any prime less than 90 and find a set r such that ∀i, f(r) ≡ 0 (mod p). For each r, add an entry (r, p) to A. Repeating this for all p in the set of primes less than 90 yields A = { (0, 2),(6, 7),(13, 17),(11, 23),(26, 29),(18, 31),(19, 41),(13, 43),(1, 53),(46, 61), (2, 67),(6, 67),(44, 67),(50, 73),(23, 79),(47, 79),(73, 79),(28, 89),(62, 89),(73, 89) }
My question is, how are the determining "r" here, by what equation are they using. prime 67 has three answers: (2,67) and (6, 67), and (44, 67). I'm not sure how they are determining the "r" here and would like to ask if anyone knows what algorithm or process they are using to determine these r values. I'm writing code to implement this step and am stuck here. Any better resources or guides would be welcome that explain how to create the pairs in this step. Thank you.
In general, i'm looking to know how to create the pairs for AFB after creating the polynimial and creating the RFB table.